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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 225 · 40 questions
TalentJR

How to solve it (Across, up, Pythagoras): Distance: across = difference of the x values, up = difference of the y values; distance = √(across² + up²). Midpoint = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). Quadrants by signs: (+, +) first, (−, +) second, (−, −) third, (+, −) fourth.

NameDateTime takenScore ___ / 40
  1. 1.What is the distance between the points (7, 14) and (16, 2)? (a) 21 (b) 16 (c) 15 (d) 225
  2. 2.What is the distance between the points (0, 7) and (24, 14)? (a) 26 (b) 25 (c) 625 (d) 31
  3. 3.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  4. 4.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
  5. 5.In which quadrant does the point (−1, −6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  6. 6.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
  7. 7.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  8. 8.What is the midpoint of the line joining (3, 13) and (5, 9)? (a) (11, 4) (b) (4, 11) (c) (8, 22) (d) (1, 2)
  9. 9.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 17 (d) 23
  10. 10.In which quadrant does the point (2, −6) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  11. 11.What is the midpoint of the line joining (0, 7) and (4, 17)? (a) (2, 5) (b) (2, 12) (c) (12, 2) (d) (4, 24)
  12. 12.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
  13. 13.In which quadrant does the point (3, 8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  14. 14.In which quadrant does the point (9, 6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  15. 15.What is the midpoint of the line joining (2, 9) and (10, 21)? (a) (15, 6) (b) (6, 15) (c) (4, 6) (d) (12, 30)
  16. 16.What is the distance between the points (1, 7) and (4, 11)? (a) 25 (b) 7 (c) 5 (d) 6
  17. 17.In which quadrant does the point (9, −5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  18. 18.What is the distance between the points (3, 2) and (19, 14)? (a) 21 (b) 20 (c) 28 (d) 400
  19. 19.What is the midpoint of the line joining (2, 11) and (14, 7)? (a) (6, 2) (b) (16, 18) (c) (9, 8) (d) (8, 9)
  20. 20.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
  21. 21.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  22. 22.What is the midpoint of the line joining (0, 7) and (8, 9)? (a) (4, 1) (b) (4, 8) (c) (8, 4) (d) (8, 16)
  23. 23.What is the distance between the points (7, 22) and (15, 7)? (a) 289 (b) 18 (c) 17 (d) 23
  24. 24.What is the distance between the points (8, 14) and (16, 8)? (a) 14 (b) 10 (c) 11 (d) 100
  25. 25.In which quadrant does the point (5, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  26. 26.What is the distance between the points (6, 16) and (15, 4)? (a) 16 (b) 225 (c) 15 (d) 21
  27. 27.What is the midpoint of the line joining (2, 1) and (4, 11)? (a) (1, 5) (b) (3, 6) (c) (6, 3) (d) (6, 12)
  28. 28.What is the midpoint of the line joining (5, 5) and (17, 3)? (a) (22, 8) (b) (4, 11) (c) (11, 4) (d) (6, 1)
  29. 29.In which quadrant does the point (2, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  30. 30.What is the distance between the points (7, 7) and (10, 3)? (a) 7 (b) 6 (c) 5 (d) 25
  31. 31.What is the distance between the points (0, 17) and (15, 9)? (a) 23 (b) 289 (c) 17 (d) 18
  32. 32.What is the distance between the points (2, 25) and (14, 9)? (a) 28 (b) 400 (c) 20 (d) 21
  33. 33.What is the midpoint of the line joining (2, 4) and (12, 0)? (a) (7, 2) (b) (14, 4) (c) (2, 7) (d) (5, 2)
  34. 34.In which quadrant does the point (−9, −5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  35. 35.What is the distance between the points (3, 3) and (15, 19)? (a) 21 (b) 400 (c) 20 (d) 28
  36. 36.What is the midpoint of the line joining (3, 12) and (9, 4)? (a) (8, 6) (b) (6, 8) (c) (3, 4) (d) (12, 16)
  37. 37.What is the midpoint of the line joining (0, 13) and (4, 9)? (a) (2, 2) (b) (2, 11) (c) (4, 22) (d) (11, 2)
  38. 38.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
  39. 39.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17
  40. 40.In which quadrant does the point (−8, 9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant

Answer key

  1. 15
  2. 25
  3. 15
  4. 10
  5. Third quadrant
  6. 20
  7. 10
  8. (4, 11)
  9. 17
  10. Fourth quadrant
  11. (2, 12)
  12. 20
  13. First quadrant
  14. First quadrant
  15. (6, 15)
  16. 5
  17. Fourth quadrant
  18. 20
  19. (8, 9)
  20. 17
  21. 15
  22. (4, 8)
  23. 17
  24. 10
  25. First quadrant
  26. 15
  27. (3, 6)
  28. (11, 4)
  29. First quadrant
  30. 5
  31. 17
  32. 20
  33. (7, 2)
  34. Third quadrant
  35. 20
  36. (6, 8)
  37. (2, 11)
  38. 13
  39. 13
  40. Second quadrant

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